The invention concerns a method of coherent demodulation for phase shift keying and a device for implementing the method.
The invention is thus applicable to transmission systems using type PSK2 or PSK4 modulation for example.
In a current demodulator known in the art, the analog signal at the intermediate frequency f.sub.i is transformed to the base band by multiplication in in-phase and quadrature channels, followed by filtering to remove image frequencies. The signal is then digitized for each channel and, after passing through a matched filter, a baseband signal is obtained, which may be represented by a complex number: EQU r.sub.k =r(kT.sub.s)=g exp(j(k.DELTA.w.sub.1 T.sub.s +.phi..sub.k))s.sub.k +n.sub.k
where:
g is the gain (loss) introduced by the channel; PA1 T.sub.s is the symbol time; ##EQU1## s.sub.k being the symbol transmitted at the instant kT.sub.s ; M representing the number of phase states and 1 being an integer corresponding to the coded bit or bits; PA1 n.sub.k is a representation of the white Gaussian noise at the instant kT.sub.s ; PA1 .DELTA.w.sub.i =2.pi..DELTA.f.sub.i corresponding to the frequency difference between the transmission and reception oscillators. PA1 Putting h.sub.k =g exp(j(k.delta.w+.phi..sub.k)) we get the condensed notation: EQU r.sub.k =h.sub.k s.sub.k +n.sub.k. PA1 a phase estimation stage based on a sequence of reference symbols transmitted at the start of each block of data: PA1 then a second order phase-locked loop stage. PA1 a circuit for phase estimation based on the reference symbols; PA1 a second order phase-locked loop. PA1 a delay circuit: PA1 a first multiplier circuit receiving at its second input the input signal of the delay circuit passed through a multiplier circuit, an adder-accumulator circuit and a conversion circuit: PA1 a synchronizing circuit for the reference sequence, connected to:
If .delta.w=.DELTA.w.sub.i T.sub.s we have: EQU r.sub.k =g exp(j(k.delta.w+.phi..sub.k))s.sub.k +n.sub.k
In demodulation based on channel estimation, the essential condition for good operation is the insertion of R reference symbols (known a priori to the receiver) every I information symbols, so as to form blocks of R+I symbols. The R reference symbols may be identical for each block or equally be constructed on the basis of one (for PSK2) or two (for PSK4) pseudorandom sequences of period N=2.sup.m -1, such that m&gt;&gt;R. The order of magnitude of R may be around ten and that of I of some tens.
If the channel is slowly varying it can be assumed that .phi..sub.k =.phi. and .delta.w.apprxeq.0, so that in fixing the origin of time for the start of each block we take: EQU h.sub.k =h.sub.R/2 =h for k.epsilon.{0, . . . R-1}
Thanks to the knowledge of the signal received in the interval [0, . . . R-1] and from the Gaussian nature of the additive noise n.sub.k, the variable h can be estimated from the maximum likelihood. This means minimizing a function L defined as follows: ##EQU2##
We can then calculate the gradient of L relative to h.sub.r and h.sub.i, with the notation h=h.sub.r +jh.sub.i : ##EQU3##
Setting G.sub.hr (L)+jG.sub.hi (L) to zero we obtain: ##EQU4##
To effect the coherent demodulation we then perform: ##EQU5## The demodulation should preserve the power of the received signal; hence the normalization by .vertline.h.vertline..
The advantage of this method of demodulation is the removal of the phase ambiguity, as well as its good resistance to Gaussian noise. It can also be noted that, once the symbol synchronization is acquired, the convergence of the phase estimator is less than the duration of a block, namely (R+I)T.sub.s iterations. The low frequency of the phase estimation makes the method inapplicable when: ##EQU6##
This means a major constraint on the drift of the oscillators.
In loop demodulation, the gradient algorithm is used to minimize an estimation function as described in the article entitled "Simultaneous adaptive estimation and decision algorithm for carrier modulation data transmission systems" by H. Kobayashi, (IEEE Transaction and communication technology; vol COM-19, June 1971, pages 268-280). This estimation function is worked out in order to obtain a decision criterion according to the maximum likelihood. EQU .psi..sub.k arg(h.sub.k)=k.delta.w+.phi..sub.k mod2.pi..
In deriving this estimation function an estimate of the phase error is obtained: EQU e.sub.k =Im(sign(z.sub.k)z.sub.k.sup.*)
with EQU z.sub.k =r.sub.k exp(-j.psi..sub.k)
and EQU .psi..sub.k+1 =.psi..sub.K +ow.sub.k -.beta.e.sub.k mod2.pi.ow.sub.k =ow.sub.k-1 -.alpha.e.sub.k mod2.pi.
where .beta. is the step of the gradient and corresponds to a loop gain. .alpha. is also a loop parameter. It may be so chosen that .alpha.=.beta..sup.2 /2.
This decision-based system does not resolve the problem of phase ambiguity. Its convergence is relatively slow when noise is significant.